Theory of light-induced effective magnetic field in Rashba ferromagnets

Motivated by recent experiments on all-optical magnetization reversal in conductive ferromagnetic thin films we use nonequilibrium formalism to calculate the effective magnetic field induced in a Rashba ferromagnet by a short laser pulse. The main contribution to the effect originates in the direct optical transitions between spin-split subbands. The resulting effective magnetic field is inversely proportional to the impurity scattering rate and can reach the amplitude of a few Tesla in the systems like Co/Pt bilayers. We show that the total light-induced effective magnetic field in ferromagnetic systems is the sum of two contributions: a helicity dependent term, which is an even function of magnetization, and a helicity independent term, which is an odd function of magnetization. The primary role of the spin-orbit interaction is to widen the frequency range for direct optical transitions.

Figure 1

The spectrum of model (1) and the direct optical transition corresponding to the frequency $\mathrm{\Omega }$ that fulfills the condition of Eq. (2).

Figure 2

(a) Feynman diagrams illustrating Born approximation that is used to derive the expression for the averaged Green's function in Eq. (12). (b) Diagrammatic representation of Eq. (13) on the vertex $\mathrm{\Gamma }$ that describes the electron diffusion. (c) Representation of the dc nonequilibrium spin polarization due to direct optical transitions as given by Eq. (10).

Figure 3

The results for $z$ component of the effective magnetic field in the units of Tesla calculated from Eqs. (5) and (16) for circularly polarized light with the helicity $\lambda$ and for two values of the parameter $\mathrm{\Delta }=m{\alpha }_{\mathrm{R}}^2$. We choose here ${\mathcal{E}}_0={10}^9$ V m, ${\varepsilon }_{\text{F}}=3.3$ eV, $M=0.3$ eV, ${\gamma }_{+}=2{\gamma }_{-}$, ${\gamma }_{-}=1$ meV, $d=0.4$ nm. The effect is restricted to a finite frequency window of Eq. (2) that essentially depends on $\mathrm{\Delta }$.